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nonlinear string equation; accelerated convergence; existence; periodic; Dirichlet boundary conditions; vibrations; damped extensive string; time-periodic solution

References:

[1] R. W. Dickey: **Infinite systems of nonlinear oscillation equations with Linear Damping**. Siam J. Appl. Math. 19 (1970), pp. 208-214. DOI 10.1137/0119019 | MR 0265654 | Zbl 0233.34014

[2] S. Klainerman: **Global existence for nonlinear wave equations**. Comm. Pure Appl. Math. 33 (1980), pp. 43--101. DOI 10.1002/cpa.3160330104 | MR 0544044 | Zbl 0405.35056

[3] P. Krejčí: **Hard Implicit Function Theorem and Small periodic solutions to partial differential equations**. Comment. Math. Univ. Carolinae 25 (1984), pp. 519-536. MR 0775567

[4] J. Moser: **A rapidly-convergent iteration method and nonlinear differential equations**. Ann. Scuola Norm. Sup. Pisa 20-3 (1966), pp. 265-315, 499-535.

[5] O. Vejvoda, et al.: **Partial differential equations: Time-periodic Solutions**. Martinus Nijhoff Publ., 1982. Zbl 0501.35001